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  • 无限大整数相加算法的C语言源代码

    忙里偷闲,终于完成了无限大整数相加算法的C语言代码,无限大整数相加算法的算法分析在这里

    500位的加法运行1000次,不打印结果的情况下耗时0.036秒,打印结果的情况下耗时16.285秒。

    下面是源码:

    #include <stdio.h>
    #include <stdlib.h>
    #include<string.h>
    #include <time.h>
    
    #define MAXNUM 1000000000000000000
    /*
    存储数据用的结构
    long int型指针(Number)指向一个long int 数组,索引值最底的位,
    为10进制数的最低18位。依次类推。
    int型数值(Length)为数组的长度。
    因为数组长度受int型最大值的限制,所以这个算法也不能真正实现“无限”。
    */
    struct BigInt{
        long long* Number;
        int Length;
    };
    
    void PrintBigInt(BigInt* bigNumber);
    
    long long pow(int x, int y);
    
    BigInt* MakeBigIntFromString(char* bigIntString);
    
    void DeleteBigInt(BigInt* bigNumber);
    
    BigInt* Add2BigInt(BigInt* n1, BigInt* n2);
    
    void main(){
    
        char* numberStr = "99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999";
        char* numberStr2 = "99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999";
        BigInt* bn = MakeBigIntFromString(numberStr);
        BigInt* bn2 = MakeBigIntFromString(numberStr2);
        double tstart, tend, tcost;
        tstart = clock();
        PrintBigInt(bn);
        PrintBigInt(bn2);
        for (int i = 0; i < 1000; i++){
            BigInt* result = Add2BigInt(bn, bn2);
            //PrintBigInt(result);
            DeleteBigInt(result);
        }
        DeleteBigInt(bn);
        DeleteBigInt(bn2);
        tend = clock();
        tcost = (double)(tend - tstart) / CLOCKS_PER_SEC;
        printf("%lf
    ", tcost);
    }
    
    BigInt* Add2BigInt(BigInt* n1, BigInt* n2){
    
        int maxLength = n1->Length;
        if (maxLength < n2->Length){
            maxLength = n2->Length;
        }
    
        /*
        加法只可能产生1位的进位,所以,只需要创建一个和最大长度相同的。
        */
        BigInt* nOut = (BigInt*)malloc(sizeof(BigInt));
        nOut->Length = maxLength;
        nOut->Number = (long long*)malloc(sizeof(long long)* nOut->Length);
        for (int i = 0; i < nOut->Length; i++){
            nOut->Number[i] = 0;
        }
        for (int i = 0; i < nOut->Length; i++){
            if (n1->Length > i){
                nOut->Number[i] += n1->Number[i];
            }
            if (n2->Length > i){
                nOut->Number[i] += n2->Number[i];
            }
    
            /*
            处理进位。最高位不需要处理。
            */
            if (i != (nOut->Length - 1)){
                if (nOut->Number[i] >= MAXNUM){
                    nOut->Number[i] -= MAXNUM;
                    nOut->Number[i + 1] = 1;
                }
            }
        }
    
        return nOut;
    
    }
    
    /*
    从高到低显示数值
    不考虑单个long long数据超出18位的情况。
    */
    void PrintBigInt(BigInt* bigNumber){
        if (bigNumber == NULL){
            return;
        }
        if (bigNumber->Length < 1){
            return;
        }
        int length = bigNumber->Length - 1;
        for (int i = length; i >= 0; i--){
            if (i != length){
                if (bigNumber->Number[i] == 0){
                    printf("000000000000000000");
                }
                else{
                    printf("%018lld", bigNumber->Number[i]);
                }
            }
            else{
                if ((*bigNumber).Number[i] != 0){
                    printf("%lld", bigNumber->Number[i]);
                }
            }
        }
        printf("
    ");
    
    }
    
    /*
    把字符串表示的数值格式化为BigInt型的结构
    字符串结束位置用表示。
    */
    BigInt* MakeBigIntFromString(char* bigIntString){
        /*获取字符串长度*/
        int cLength = strlen(bigIntString);
        BigInt* outBigInt = (BigInt*)malloc(sizeof(BigInt));
        if (cLength % 18 != 0){
            outBigInt->Length = cLength / 18 + 1;
        }
        else{
            outBigInt->Length = cLength / 18;
        }
        if (outBigInt->Length == 0){
            outBigInt->Length == 1;
            outBigInt->Number = (long long *)malloc(sizeof(long long));
            outBigInt->Number[0] = 0;
    
            return outBigInt;
        }
        outBigInt->Number = (long long *)malloc(sizeof(long long)* outBigInt->Length);
        for (int i = 0; i < outBigInt->Length; i++){
            outBigInt->Number[i] = 0;
        }
    
        int powNum = 0;
        int numPos = 0;
        for (int i = cLength - 1; i >= 0; i--){
            powNum = (cLength - 1 - i) % 18;
            numPos = (cLength - 1 - i) / 18;
            outBigInt->Number[numPos] += (bigIntString[i] - 48) * pow(10, powNum);
        }
    
        return outBigInt;
    }
    
    /*
    简单的幂函数
    x y 都必须为正整数
    */
    long long pow(int x, int y){
        if (x == 0 || x < 0 || y < 0){
            return 0;
        }
        if (x == 1 || y == 0){
            return 1;
        }
        long long outNum = x;
    
        for (int i = 1; i < y; i++){
            outNum = outNum * x;
        }
    
        return outNum;
    }
    
    void DeleteBigInt(BigInt* bigNumber){
        if (bigNumber != NULL){
            if (bigNumber->Number != NULL){
                free(bigNumber->Number);
            }
            free(bigNumber);
        }
    }
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  • 原文地址:https://www.cnblogs.com/liu-binq63/p/4550401.html
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